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3 years ago

13. The numerator of a rational number is 3 less than the denominator. If the denominator is

Mathematics

1 answer:

g100num [7]3 years ago

5 0

Fraction = 4/7

Step by step Explanation

Let the denominator be x.

Numerator = 3 less than denominator

denominator = x

Numerator = (x – 3)

Now, Adding 5 to denominator

adding 2 to numerator.

Numerator = (x – 3 + 2)

Denominator = (x + 5)

(x – 3 + 2)/(x + 5)

According to the question

(x – 3 + 2)/(x + 5) = 1/2

(x – 1)/(x + 5) = 1/2

2(x – 1) = 1(x + 5)

2x – 2 = x + 5

2x – x = 5 + 2

x = 7

So,

=> Denominator x = 7

=> Numerator (x – 3) => (7 – 3) = 4

= > Fraction = 4/7

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The vertices of a triangle ABC are A(7, 5), B(4, 2), and C(9, 2). What is measure of angle ABC? 30° 45° 56.31° 78.69°

GenaCL600 [577]

The measure of angle ABC is 45°

Explanation

Vertices of the triangle are: A(7, 5), B(4, 2), and C(9, 2)

According to the diagram below....

Length of the side BC (a) $=\sqrt{(4-9)^2+(2-2)^2}= \sqrt{25}= 5$

Length of the side AC (b) $= \sqrt{(7-9)^2 +(5-2)^2}= \sqrt{4+9}=\sqrt{13}$

Length of the side AB (c) $= \sqrt{(7-4)^2 +(5-2)^2} =\sqrt{9+9}=\sqrt{18}$

We need to find ∠ABC or ∠B . So using Cosine rule, we will get...

$cosB= \frac{a^2+c^2-b^2}{2ac} \\ \\ cos B= \frac{(5)^2+(\sqrt{18})^2-(\sqrt{13})^2}{2*5*\sqrt{18} }\\ \\ cosB= \frac{25+18-13}{10\sqrt{18}} =\frac{30}{10\sqrt{18}}=\frac{3}{\sqrt{18}}\\ \\ cosB=\frac{3}{3\sqrt{2}} =\frac{1}{\sqrt{2}}\\ \\ B= cos^-^1(\frac{1}{\sqrt{2}})= 45 degree$

So, the measure of angle ABC is 45°

7 0

3 years ago

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mojhsa [17]

Answer:

2 pages per minute

Step-by-step explanation:

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4 0

3 years ago

7 divided by 4 x + 3 Y + 4 divided / 4 x minus 3 Y is equal to 5 / 4

DerKrebs [107]

9514 1404 393

Answer:

(x, y) = (4, 4)

Step-by-step explanation:

If you attempt to solve this by clearing fractions, you end up with an extraneous solution. Here, we'll solve the linear equations ...

7a +4b = 5/4

8b -14a = 3/2

where a = 1/(4x+3y) and b = 1/(4x-3y)

Dividing the second equation by 2 and adding the first, we have ...

(7a +4b) +1/2(8b -14a) = (5/4) +1/2(3/2)

8b = 8/4

b = 1/4

Substituting into the first equation gives ...

7a +4/4 = 5/4

a = 1/28

Now, we can get back to solving for x and y.

4x +3y = 1/a = 28

4x -3y = 1/b = 4

8x = 32 . . . . . . . . . add the two equations

x = 4

3y = 28 -4x = 28 -4(4) = 12 . . . . . use x in the equation for 'a'; rearrange

y = 4 . . . . divide by 3

The solution to the system of equations is (x, y) = (4, 4).

_____

Additional comment

If you graph these equations, you find they describe hyperbolas that intersect at (0, 0) and (4, 4). The "solution" (0, 0) is extraneous, as both equations are undefined there.

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2 years ago

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Rainbow [258]

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2 years ago

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What's the area of a sector of a circle that has a diameter of 10 in. if the length of the arc is 10 in.?

jasenka [17]

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3 years ago

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